Question

Area of ΔPCD = 10 cm². Find the area of ΔADQ and parallelogram ABCD.

Answer 1

Given:

• Area of triangle PCD = 10 cm²
• ABCD is a parallelogram

We know that,

If a triangle and parallelogram are drawn on the same base and between the same parallel lines, then the area of the triangle is half of the area of the parallelogram.

Since, ΔPCD and || gm ABCD are on same base DC and between same parallels AB and DC.

∴ ar(ΔPCD) = `1/2` ar(|| gm ABCD)   ...(i)

Also, ΔADQ and || gm ABCD are on same base AD and between same parallels AD and BQ.

∴ ar(ΔADQ) = `1/2` ar(|| gm ABCD)   ...(ii)

⇒ ar(|| gm ABCD) = 2 × ar(ΔADQ) = 2 × 10 = 20 cm²

From (i) and (ii),

Area(ΔADQ) = Area(ΔPCD) = 10 cm²

Hence proved.